Question 804220
x and y dimensions.
x is divided into three equal lengths, so {{{(1/3)x}}}.


Each court part is area {{{(1/3)xy}}}, and the entire rectangular area for these court parts is {{{xy=1500}}} {{{ft^2}}}.


Total fencing used is {{{x+y+2y=x+3y=800}}} ft.


The system is symbolically described with equations:
{{{x+3y=800}}} and {{{xy=1500}}}.
Fence length equation allows {{{x=800-3y}}}.  Substitute...
{{{(800-3y)y=1500}}}
{{{800y-3y^2=1500}}}
{{{800y-1500-3y^2=0}}}
{{{-800y+1500+3y^2=0}}} when multiplied both sides by -1.
{{{3y^2-800y+1500=0}}}


General Solution to Quadratic Formula:
{{{y=(800+sqrt(800^2-4*3*(1500)))/(2*3)}}}
{{{y=(800+sqrt(622000))/(2*3)}}}


scratchwork...8*77750=8*50*1555=8*50*5*311...
2*2*2*2*5*5*5*311...
sqrt(622000)=20*sqrt(5*311)...


{{{y=(800+20*sqrt(1555))/(2*3)}}}
{{{y=(400+10*sqrt(1555))/3}}} relatively simple radical form.


You can finish for finding x value.